This will work for most recoil starts if you dont know what the length is, especially zone starts up on the handle etc.
Feed cord through the knob (and or any fittings) first before you start if youve got a long roll. Wind it up till the spring binds then back it off (1/2 to a full turn) a bit, You dont want spring bind to be the thing that stops the cord pulling out. Hold the spring wound up and get the cord in and tie it off (awl or seal picks are handy). Relase it slowly and let it pull cord in until it binds up and reel is full. Then pull a little out so spring tension will hold the knob and the cord is not binding on something first leaving knob flopping. Then tie it off to the knob and cut cord.
The early side pull start Briggs motors are different. Pull them apart. Fill with cord etc. Then put it back together, pre load the spring enough to hold the cord in and put the bottom cover back on. Dont pop that cap off the bottom if its got tension on the spring.
The 3.5Hp side pull Quantums would almost have to be the worst things in the world.
I might like to also say that youre mad. $70 is way too cheap. Even $30 for that other one. Minimum $100. Ive got a couple here that i would let go for $80 but they aint right, old as the hills, bad bar blades and blow a bit of smoke.
Any primer or choke start 4 stroke. If i cant get $150+ ( i like $170 or more) i pull the motor off and put it on something i will get that money for.
With what you said you did. A mower shop would charge more than my asking price for a mower for that repair.
'But ive only got $50' you hear them say.
"Well if you head down the super market and lash out on few pairs of scissors you could get some friends over and make a day of it." That lets em know you mean business.